@article{Argyros_2007, title={Approximating solutions of equations using Newton’s method with a modified Newton’s method iterate as a starting point}, volume={36}, url={https://ictp.acad.ro/jnaat/journal/article/view/2007-vol36-no2-art2}, DOI={10.33993/jnaat362-862}, abstractNote={<pre>In this study we are concerned with the problem of approximating a</pre><pre> locally unique solution of an equation in a Banach space setting</pre><pre> using Newton’s and modified Newton’s methods. We provide weaker</pre><pre> convergence conditions for both methods than before [6]-[8].</pre><pre> Then, we combine Newton’s with the modified Newton’s method to</pre><pre> approximate locally unique solutions of operator equations in a</pre><pre> Banach space setting. Finer error estimates, a larger convergence</pre><pre> domain, and a more precise information on the location of the</pre><pre> solution are obtained under the same or weaker hypotheses than</pre><pre> before [6]-[8]. Numerical examples are also provided.</pre>}, number={2}, journal={Rev. Anal. Numér. Théor. Approx.}, author={Argyros, Ioannis}, year={2007}, month={Aug.}, pages={123–137} }